Coulomb potential and the paradoxes of PT-symmetrization
Miloslav Znojil
TL;DR
This paper explores an alternative quantum Coulomb model with unique symmetry properties, offering exact solutions and new insights into PT-symmetrization paradoxes in quantum mechanics.
Contribution
It introduces a novel quantization approach that redefines the role of symmetries in quantum Coulomb problems, expanding theoretical understanding.
Findings
The alternative model exhibits similar spectral and scattering properties as the standard Coulomb problem.
The model is exactly solvable, demonstrating its mathematical robustness.
The paper clarifies the role of symmetries in PT-symmetric quantum systems.
Abstract
Besides the standard quantum version of the Coulomb/Kepler problem, an alternative quantum model with not too dissimilar phenomenological (i.e., spectral and scattering) as well as mathematical (i.e., exact-solvability) properties may be formulated and solved. Several aspects of this model are described. The paper is made self-contained by explaining the underlying innovative quantization strategy which assigns an entirely new role to symmetries.
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